{"id":14033,"date":"2026-07-18T22:03:24","date_gmt":"2026-07-18T22:03:24","guid":{"rendered":"https:\/\/www.vedprep.com\/exams\/?p=14033"},"modified":"2026-07-18T22:03:24","modified_gmt":"2026-07-18T22:03:24","slug":"trapezoidal-rule-gate","status":"publish","type":"post","link":"https:\/\/www.vedprep.com\/exams\/gate\/trapezoidal-rule-gate\/","title":{"rendered":"Trapezoidal Rule for Gate: Trapezoidal Rule Mastery: 5"},"content":{"rendered":"
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Trapezoidal Rule Mastery: 5 Proven Tips For GATE Success<\/h1>\n<\/header>\n
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The trapezoidal rule for GATE<\/strong> is a cornerstone of numerical analysis, helping engineers and scientists approximate integrals efficiently. Whether you’re preparing for GATE or other competitive exams like CSIR NET or IIT JAM, mastering this technique can significantly boost your problem-solving skills.<\/p>\n

Trapezoidal Rule for Gate: Key Concepts<\/h2>\n

Numerical integration is a critical topic in GATE exams, particularly in subjects like Computer Science, Engineering, and Mathematics. The trapezoidal rule for GATE<\/strong> is one of the most straightforward yet powerful methods for approximating definite integrals. It divides the area under a curve into trapezoids, sums their areas, and provides a close approximation of the integral. This method is widely used in real-world applications, including physics simulations, engineering calculations, and data analysis.<\/p>\n

The Trapezoidal Rule Formula<\/strong> Explained<\/h2>\n

The core of the trapezoidal rule for GATE<\/strong> lies in its formula:<\/p>\n

\"Trapezoidal<\/div>\n

Here, h<\/code> is the width of each subinterval, and f(x_i)<\/code> are the function values at the points x_i<\/code>. The formula is derived by approximating the area under the curve using trapezoids, ensuring a balance between simplicity and accuracy.<\/p>\n

Step-by-Step Guide: Applying the Trapezoidal Rule for GATE<\/strong><\/h2>\n

Let\u2019s walk through a practical example to solidify your understanding of the trapezoidal rule for GATE<\/strong>. Suppose we want to approximate the integral of f(x) = x^2<\/code> from x = 0<\/code> to x = 2<\/code>.<\/p>\n

Step 1: Divide the Interval<\/h3>\n

First, divide the interval [0, 2] into n<\/strong> equal subintervals. For simplicity, let\u2019s use n = 4<\/strong>, giving us a subinterval width of h = (2 - 0) \/ 4 = 0.5<\/code>. The points of subdivision are x_0 = 0, x_1 = 0.5, x_2 = 1, x_3 = 1.5, x_4 = 2<\/code>.<\/p>\n

Step 2: Evaluate Function Values<\/h3>\n

Next, evaluate the function f(x)<\/code> at these points:<\/p>\n